Adjoint Error Correction on Unstructured Finite Volume Solvers

One of the major applications of the adjoint method is the improvement in the order of accuracy of integral quantities obtained from CFD simulations. Although the theory requires the use of a smooth interpolation of the solution, this has seldom been used with unstructured finite volume solvers. In this paper, the adjoint based correction is applied to output functionals obtained using finite volume method on unstructured meshes. A smoothing spline based on a $C1$continuous representation of the discrete solution is employed to reduce the random noise in the solution and to improve the rate of convergence of the derivatives. Tests performed on randomly perturbed meshes in 1-D showed fourth-order convergence of output functionals obtained from second-order solution, corrected using the truncation error obtained using the smoothing spline and second-order accurate adjoint solution. The extension of this method to 2-D problems showed superconvergence for output functionals and improvements over existing results.